There has recently been a dramatic renewal of interest in hadron spectroscopy and charm physics. This renaissance has been driven in part by the discovery of a plethora of charmonium-like XYZ states at BESIII and B factories, and the observation of an intriguing proton-antiproton threshold enhancement and the possibly related X(1835) meson state at BESIII, as well as the threshold measurements of charm mesons and charm baryons. We present a detailed survey of the important topics in tau-charm physics and hadron physics that can be further explored at BESIII during the remaining operation period of BEPCII. This survey will help in the optimization of the data-taking plan over the coming years, and provides physics motivation for the possible upgrade of BEPCII to higher luminosity.

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We observe a narrow enhancement near 2m(p) in the invariant mass spectrum of pp pairs from radiative J/psi-->gammapp decays. No similar structure is seen in J/psi-->pi(0)pp decays. The results are based on an analysis of a 58 x 10(6) event sample of J/psi decays accumulated with the BESII detector at the Beijing electron-positron collider. The enhancement can be fit with either an S- or P-wave Breit-Wigner resonance function. In the case of the S-wave fit, the peak mass is below 2m(p) at M=1859(+3)(-10) (stat)+5-25(syst) MeV/c(2) and the total width is Gamma<30 MeV/c(2) at the 90% confidence level. These mass and width values are not consistent with the properties of any known particle.

The decays of J/psi --> etaphif(0)(980)[eta --> gammagamma, phi --> K(+) K(-), f(0)(980) --> pi(+)pi(-)] are analyzed using a sample of 5.8 x 10(7) J/psi events collected with the BESII detector at the Beijing Electron-Positron Collider. A structure at around 2.18 GeV/c(2) with about 5 sigma significance is observed in the phif(0)(980) invariant mass spectrum. A fit with a Breit-Wigner function gives the peak mass and width of m = 2.186+/-0.010(stat)+/-0.006(syst) GeV/c(2) and Gamma = 0.065+/-0.023(stat)+/-0.017(syst) GeV/c(2), respectively, which are consistent with those of Y(2175), observed by the BABAR Collaboration in the initial-state radiation process e(+)e(-) --> gamma(ISR) phif(0)(980). The production branching ratio is determined to be Br(J/psi --> etaY(2175))Br(Y(2175)- -> phif(0)(980))Br(f(0)(980) --> pi(+)pi(-)) = [3.23+/-0.75(stat)+/-0.73(syst)] x 10(-4), assuming that the Y(2175) is a 1(--) state.

The number of J/ψ events collected with the BES detector at the BEPC from June 12 to July 28, 2009 is determined to be (225.3±2.8)×10 6 using J/ψ →inclusive events, where the uncertainty is the systematic error and the statistical one is negligible.